solves the continuous algebraic Riccati equation - Maple Help

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LinearAlgebra[CARE] - solves the continuous algebraic Riccati equation

Calling Sequence

CARE(A, B, Q, R, S, options, outopts)

Parameters

A

-

Matrix(square)

B

-

Matrix

Q

-

Matrix

R

-

(optional) Matrix(square)

S

-

(optional) Matrix

options

-

(optional) constructor options for the result objects and/or equation(s) of the form keyword = value, where keyword is one of haveB or output

outopts

-

(optional) equation(s) of the form outputoptions[o] = list, where o is one of X, L or G

Description

• 

The CARE command solves the continuous algebraic Riccati equation,

A+ .X+X.AS+X.B.R-1.S+X.B+ +Q=0

• 

The optional Matrix arguments R and S default respectively to the identity Matrix and the zero Matrix.

• 

This routine operates in the real floating-point domain. Hence, the entries in the Matrix arguments must necessarily be of type numeric.

Examples

withLinearAlgebra:

a:=Matrix3,2,1,1:

b:=Matrix0,1:

c:=Matrix1,1:

r:=Matrix3:

CAREa,b,c%T.c,r,output=X,L

0.5895174372762621.821574724886091.821574724886098.81883980692312,3.42578096594334+0.I1.32083158810045+0.I

(1)

a:=Matrix0,1,0,0:

q:=Matrix1,0,0,2:

b:=Matrix0,0,0,1:

CAREa,b,q

2.000000000000001.000000000000001.000000000000002.00000000000000

(2)

CAREa,b,q,output=X

2.000000000000001.000000000000001.000000000000002.00000000000000

(3)

CAREa,b,q,output=X,L,rcond

2.000000000000001.000000000000001.000000000000002.00000000000000,0.771362440687311+0.I0.788573854448794+0.I,0.427050982331351692

(4)

See Also

copyright, DARE, LinearAlgebra, LyapunovSolve, Matrix, SylvesterSolve, Vector


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